Data card verification system

ABSTRACT

A method of verifying a pair of correspondents in electronic transaction, the correspondents each including first and second signature schemes and wherein the first signature scheme is computationally more difficult in signing than verifying and the second signature scheme is computationally more difficult in verifying than signing. The method comprises the step of the first correspondent signing information according to the first signature scheme and transmitting the first signature to the second correspondent, the second correspondent verifying the first signature received from the first correspondent, wherein the verification is performed according to the first signature scheme. The second correspondent then signs information according to the second signature scheme and transmits the second signature to the first correspondent, the first correspondent verifies the second signature received from the second correspondent, wherein the verification is performed according to the second signature algorithm; the transaction is rejected if either verification fails. The method thereby allows one of the correspondents to participate with relatively little computing power while maintaining security of the transaction.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.10/185,042 filed on Jul. 1, 2002, now U.S. Pat. No. 7,472,276, which isa divisional of IJ.S. patent application Ser. No. 09/716,223 filed onNov. 21, 2000, now abandoned, which is a divisional of U.S. patentapplication Ser. No. 09/016,926 filed on Feb. 2, 1998 and issued underU.S. Pat. No. 6,178,507, which claims priority from United KingdomPatent Application No. 9702152.1 filed on Feb. 3, 1997 all of which arehereby incorporated by reference.

BACKGROUND OF THE INVENTION

It has become widely accepted to conduct transactions such as financialtransactions or exchange of documents electronically. Automated tellermachines (ATMs) and credit cards are widely used for personaltransaction and as their use expands so too does the need to verify suchtransactions increase. A smart card is somewhat like a credit card andincludes some processing and storage capability. Smart cards are proneto fraudulent misuse. For example by a dummy terminal which is used toglean information from an unsuspecting user. Thus, before any exchangeof critical information takes place between either a terminal and smartcard or vice versa it is necessary to verify the authenticity of theterminal as well as the card. One of these verification may take theform of “signing” an initial transaction digitally so that theauthenticity of the transaction can be verified by both parties involvedin the subsequent session. The signature is performed according to aprotocol that utilizes a random message, i.e. the transaction and asecret key associated with the party.

The signature must be performed such that the party's secret key cannotbe determined. To avoid the complexity of disturbing secret keys, it isconvenient to utilize a public key encryption scheme in the generationof the signature. Such capabilities are available where the transactionis conducted between parties having access to the relatively largecomputing resources, but it is equally important to facilitate suchtransactions at an individual level where more limited computingresources available, as in the smart card.

Transaction cards or smart cards are now available with limitedcomputing capacity, but these are not sufficient to implement existingdigital signature protocols in a commercially viable manner. As notedabove, in order to generate a verification signature it is necessary toutilize a public key inscription scheme. Currently, most public keyschemes are based on RSA, but the DSS and the demand for a more compactsystem are rapidly changing this. The DSS scheme, which is animplementation of a Diffie-Hellman public key protocol, utilizes the setof integers Z_(p) where p is a large prime. For adequate security, pmust be in the order of 512 bits, although the resultant signature maybe reduced mod q, where q divides p−1, and may be in the order of 160bits.

An alternative encryption scheme which was one of the first fullyfledged public key algorithms and which works for encryption as well asfor digital signatures is known as the RSA algorithm. RSA gets itssecurity from the difficulty of factoring large numbers. The public andprivate keys are functions of a pair of large (100 to 200 digits or evenlarger) of prime numbers. The public key for RSA encryption is n, theproduct of the two primes p and q where p and q must remain secret and ewhich is relatively prime to (p−1)×(q−1). The encryption key d is equalto e⁻¹ (mod(p−1)×(q−1)). Note that d and n are relatively, prime.

To encrypt a message m, first divide it into a number of numericalblocks such that each block is a unique representation modulo n, thenthe encrypted message block c_(i) is simply m_(i) ^(e) (mod n). Todecrypt a message take each encrypted block c_(i) and computem_(i)=c_(i) ^(d) (mod n).

Another encryption scheme that provides enhanced security at relativelysmall modulus is that utilizing elliptic curves in the finite field2^(m). A value of m in the order of 155 provides security comparable toa 512 bit modulus DSS and therefore offers significant benefits inimplementation.

Diffie-Hellman public key encryption utilizes the properties of discretelogs so that even if a generator β and the exponentiation β^(k) isknown, the value of k cannot be determined. A similar property existwith elliptic curves where the addition of two points on any curveproduces a third point on the curve. Similarly, multiplying a point P onthe curve by an integer k produces a further point on the curve. For anelliptic curve, the point kP is simply obtained by adding k copies ofthe point P together.

However, knowing the starting point and the end point does not revealthe value of the integer k which may then be used as a session key forencryption. The value kP, where P is an initial known point is thereforeequivalent to the exponentiation β^(k). Furthermore, elliptic curvecrypto-systems offer advantages over other key crypto-systems whenbandwidth efficiency, reduced computation and minimized code space areapplication goals.

Furthermore, in the context of a smart card and an automated tellermachine transaction, there are two major steps involved in theauthentication of both parties. The first is the authentication of theterminal by the smart card and the second is the authentication of thesmart card by the terminal. Generally, this authentication involves theverification of a certificate generated by the terminal and received bythe smart card and the verification of a certificate signed by the smartcard and verified by the terminal. Once the certificates have beenpositively verified the transaction between the smart card and theterminal may continue.

Given the limited processing capability of the smart card, verificationsand signature processing performed on the smart card axe generallylimited to simple encryption algorithms. A more sophisticated encryptionalgorithm is generally beyond the scope of the processing capabilitiescontained within the smart card. Thus, there exist a need for asignature verification and generation method which may be implemented ona smart card and which is relatively secure.

SUMMARY OF THE INVENTION

This invention seeks in one aspect to provide a method of dataverification between a smart card and a terminal.

In accordance with this aspect there is provided a method for verifyinga pair of participants in an electronic transaction, comprising thesteps of verifying information received by the second participant fromthe first participant, wherein the verification is performed accordingto a first signature algorithm;

verifying information received by the first participant from the secondparticipant, wherein the verification is performed according to a secondsignature algorithm; and whereby the transaction is rejected if eitherverification fails.

The first signature algorithm may be one which is computationally moredifficult in signing than verifying, while the second signaturealgorithm is more difficult in verifying than signing. In such anembodiment the second participant may participate with relatively littlecomputing power, while security is maintained at a high level.

In a further embodiment, the first signature algorithm is based on anRSA, or DDS type algorithm, and the second signature algorithm is basedon an elliptic curve algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

An embodiment of the invention will now be described by way of exampleon the reference to the accompanying drawings, in which,

FIG. 1 a is a schematic representations showing a smart card andterminal;

FIG. 1 b is a schematic representations showing the sequence of eventsperformed during the verification process in a smart card transactionsystem; and

FIG. 2 is a detailed schematic representation showing a specificprotocol.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT

Referring to FIG. 1( a), a terminal 100 is adapted to receive a smartcard 102. Typically, insertion of the card 102 into the terminalinitiates a transaction. Mutual authentication between the terminal andthe card is then performed as shown in FIG. 1 b. In very general terms,this mutual authentication is performed according to a“challenge-response” protocol. Generally, card transmits information tothe terminal, the terminal 100 signs information with an RSA basedalgorithm 112 and is then sent to the card 102, which verifies theinformation with an RSA based algorithm 114. The information exchange116 between the card and the terminal also includes informationgenerated by the card which is sent to the terminal to be signed by theterminal with an RSA algorithm and returned to the card to be verifiedutilizing a RSA algorithm. Once the relevant verification has beenperformed 118, a further step is performed where information is signedby the card using an elliptic curve encryption protocol 120 andsubmitted to the terminal to be verified 124 by the terminal utilizingan elliptic curve based protocol. Similarly, the information exchange122 between the card and the terminal may include information generatedby the terminal which is sent to the card to be signed by the card andreturned to the terminal for verification. Once the appropriateinformation has been verified 126 the further transactions between theterminal and card may proceed 128.

Referring now to FIG. 2, a detailed implementation of the mutualauthentication of the terminal and the card, according to the“challenged-response” protocol is shown generally by numeral 200. Theterminal 100 is first verified by the card 102 and the card is thenverified by the terminal. The terminal first sends to the card acertificate C₁, 20 containing its ID, T_(ID), and public informationincluding the public key. The certificate 20 may be also signed by acertifying authority (CA) so that the card may verify the association ofthe terminal ID T_(ID) with the public key received from the terminal.The keys used by the terminal and the CA in this embodiment may both bebased on the RSA algorithm.

With the RSA algorithm each member or party has a public and a privatekey, and each key has two parts. The signature has the form:—S=m ^(d)(mod n)where:

m is the message to be signed;

n a public key is the modulus and is the product of two primes p and q;

e the encryption key chosen at random and which is also public is anumber chosen to be relatively prime to (p−1)×(q−1); and

d the private key which is congruent to e⁻¹(mod (p−1)×(q−1)).

For the RSA algorithm, the pair of integers (n,e) are the public keyinformation that is used for signing. While, the pair of integers (d,n)may be used to decrypt a message which has been encrypted with thepublic key information (n,e).

Referring back to FIG. 2, the numbers n and e are the public keys of theCA and may be set as system parameters. The public key e may be eitherstored in the smart card or in an alternate embodiment hardwired into anlogic circuit in the card. Furthermore, by choosing e to be relativelysmall, ensures that the exponentiation may be carried out relativelyquickly.

The certificate 20 C₁ is signed by the CA and has the parameters (n,e).The certificate contains the terminal ID T_(id), and the terminal publickey information T_(n) and T_(e) which is based on the RSA algorithm. Thecertificate C₁ is verified 24 by the card extracting T_(ID), T_(m),T_(c). This information is simply extracted by performing C₁ ^(e) mod n.The card men authenticates the terminal by generating a random numberR1, 26, which it transmits to the terminal. The terminal signs themessage R1 using its secret key T_(d) by performing R1 ^(T), MODT_(n) togenerate the value C₂, 28. Once again the key used by the terminal is anRSA key which has been originally created in such a way that the publickey T_(c) consist of a small possibly system wide parameter having avalue 3, while the other part of the public key is the modulus T_(a)which would be associated with the terminal. The terminals private keyT_(d) cannot be small if it corresponds to a small public key T_(e). Inthe case of the terminal, it does not matter whether the private keyT_(d) is chosen to be large as the terminal has the required computingpower to perform the exponentiation relative quickly.

Once the terminal has calculated the value C₂, 28, it generates a secretrandom number R2, 29 the terminal sends both R2 and C₂, 32 to the card.The card then performs a modular exponentiation 34 on the signed valueC₂ with the small exponent T_(t), using the terminal's modulus T_(n).This is performed by calculating R1′=C₂ ^(Tc) mod T_(n). If R1′ is equalto R1, 36 then the card knows that it is dealing with the terminal whoseID T_(ID) is associated 38 with the modulus T_(n). The card generallycontains a modulo arithmetic processor (not shown) to perform the aboveoperation.

The secret random number R2 is signed 40 by the card and returned to theterminal along with a certificate signed by the CA which relates thecard ID to its public information. The signing by the card is performedaccording to an elliptic curve signature algorithm.

The verification of the card proceeds on a similar basis as theverification of the terminal, however, the signing by the card utilizesan elliptic curve encryption system.

Typically for an elliptic curve implementation a signature component shas the form:—s=ae÷k (mod n)

where:

-   -   is a point on the curve which is a predefined parameter of the        system;    -   k is a random integer selected as a short term private or        session key, and has a corresponding short term public key R=kP;    -   a is the long term private key of the sender(card) and has a        corresponding public key aP=Q;    -   e is a secure hash, such as the SHA hash function, of a message        m (R2 in this case) and short term public key R; and

n is the order of the curve.

For simplicity it will be assumed that the signature component s is ofthe form s=ae+k as discussed above although it will be understood thatother signature protocols may be used.

To verify the signature sP−eQ must be computed and compared with R. Thecard generates R, using for example a field arithmetic processor (notshown). The card sends to the terminal a message including m, s, and R,indicated in block 44 of FIG. 2 and the signature is verified by theterminal by computing the value (sP−eQ) 46 which should correspond tokP. If the computed values correspond 48 then the signature is verifiedand hence the card is verified and the transaction may continue.

The terminal checks the certificate, then it checks the signature of thetransaction data which contains R2, thus authenticating the card to theterminal. In the present embodiment the signature generated by the cardis an elliptic curve signature, which is easier for the card togenerate, but requires more computation by the terminal to verify.

As is seen from the above equation, the calculation of s is relativelystraightforward and does not require significant computing power.However in order to perform the verification it is necessary to computea number of point multiplications to obtain sP and eQ, each of which iscomputationally complex. Other protocols, such as the MQV protocolsrequire similar computations when implemented over elliptic curves whichmay result in slow verification when the computing power is limited.However this is generally not the case for a terminal.

Although an embodiment of the invention has been described withreference to a specific protocol for the verification of the terminaland for the verification of the card, other protocols may also be used.

1. A non-transitory computer readable medium comprising computerexecutable instructions for verifying authenticity of messages exchangedbetween a pair of correspondents in an electronic transaction conductedover a data transmission system, said correspondents each includingrespective signing and verifying portions of a first signature schemeand a second signature scheme different to said first scheme andutilizing an elliptic curve cryptosystem, said computer executableinstructions comprising instructions for a first of said correspondents:obtaining a first signed message from a second of said correspondents,said first signed message having been generated by one of said first andsecond correspondents signing a message according to a signing portionof one of said signature schemes associated with said one of said firstand second correspondents; utilizing said verifying portion of said onesignature scheme to verify said first signed message; signing a messageby utilizing said signing portion of the other of said signature schemesto provide a second signed message; sending said second signed messageto said second of said correspondents to enable said second of saidcorrespondents to verify said second signed message by utilizing saidverifying portion of said other of said signature schemes; and rejectingsaid transaction if either verification fails; wherein signing one ofsaid signed messages and verification of one of said signed messages areperformed according to said second signature scheme utilizing theelliptic curve cryptosystem.
 2. A non-transitory computer readablemedium according to claim 1, wherein said first signature scheme iscomputationally more difficult in signing than verifying, while saidsecond signature scheme is computationally more difficult in verifyingthan signing, thereby allowing one of said correspondents to participatewith relatively little computing power while maintaining security ofsaid transaction.
 3. A non-transitory computer readable medium accordingto claim 1, wherein said first digital signature scheme is an RSA typescheme.
 4. A non-transitory computer readable medium according to claim1, wherein said first digital signature scheme is a DSS type scheme. 5.A non-transitory computer readable medium comprising computer executableinstructions for verifying authenticity of messages exchanged between apair of correspondents in an electronic transaction conducted over adata transmission system, said correspondents each including respectivesigning and verifying portions of a first signature scheme and a secondsignature scheme, different from said first scheme and utilizing anelliptic curve cryptosystem, said computer executable instructionscomprising instructions for a first of said correspondents: obtaining afirst certificate C1 including a public key and identificationinformation of a second correspondent from one of said first and secondcorrespondents; verifying said first certificate C1 and extracting saidpublic key and said identification information therefrom; generating afirst challenge R1 and transmitting said first challenge R1 to saidsecond correspondent; receiving from said second correspondent, a secondchallenge R2 generated by said second correspondent and a secondcertificate C2, said second certificate C2 having been generated bysigning said first challenge R1 in accordance with said signing portionof one of said signature schemes; verifying said second certificate C2in accordance with said verifying portion of said one of said signatureschemes; signing said second challenge R2 in accordance with saidsigning portion of the other of said signature schemes to provide athird certificate; sending said third certificate to said secondcorrespondent to enable said second correspondent to verify said thirdcertificate in accordance with said verifying portion of said other ofsaid signature schemes; and rejecting said transaction if verificationof either signature fails.
 6. A non-transitory computer readable mediumaccording to claim 5, wherein signing one of said first and secondchallenges and verification of one of said signatures are performedaccording to said second signature scheme utilizing the elliptic curvecryptosystem.
 7. A non-transitory computer readable medium according toclaim 5, wherein said first signature scheme is computationally moredifficult in signing than verifying, while said second signature schemeis computationally more difficult in verifying than signing, therebyallowing one of said correspondents to participate with relativelylittle computing power while maintaining security of said transaction.